Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If a = 3 and b = 4, what is c?

Back

c = 5 (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

What is the formula for finding the hypotenuse?

Back

The formula is a² + b² = c².

Front

If a = 5 and b = 12, what is the length of the hypotenuse?

Back

c = 13 (5² + 12² = 25 + 144 = 169, so c = √169 = 13).

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

Use the Pythagorean Theorem: if a² + b² = c² holds true, then the triangle is a right triangle.

Front

What is the distance between two points in a right triangle?

Back

The distance can be found using the Pythagorean Theorem, treating the two points as the endpoints of the legs of a right triangle.

Front

If Jane walks 6 blocks east and Miguel walks 8 blocks north, how far apart are they?

Back

10 blocks (using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100, so distance = √100 = 10).

Front

What are the legs of a right triangle?

Back

The legs are the two sides that form the right angle.